Quantum Information Theory

Though quantum theory is already more than hundred years old, the physics of quantum information is a relatively young field of research. It aims at exploring the physical foundations of information and at developing efficient methods for processing quantum information. The questions driving this research field reflect a profound change in the general attitude towards the fundamental aspects of quantum theory. So far, research on the foundations of quantum theory has mainly been concerned with the theoretical exploration of those particular features which distinguish quantum theory from classical physics. One of the main intentions of this new research area is to exploit these specific features for technological purposes. Thereby characteristic quantum phenomena, such as entanglement, the linear superposition principle and the resulting specific quantum correlations, play an important role. However, these characteristic quantum phenomena are rather fragile. They can be destroyed easily by uncontrollable couplings to an environment. Thus, overcoming the resulting phenomenon of decoherence is a major task which has to be solved in order to achieve significant quantum technological advances.

By now quantum information has become an interdisciplinary subject which attracts not only physicists but also researchers from other communities, most prominently computer scientists and electrical engineers. For a discussion of some basic problems and methods in this research field see for example

G. Alber, T. Beth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, Berlin, 2001)
D. Bouwmeester, A. Ekert, A. Zeilinger, The Physics of Quantum Information (Springer, Berlin, 2000)

In our group, we currently investigate e.g. the following topics:

Measurement-Induced Chaos with Entangled States

The dynamics of an ensemble of identically prepared two-qubit systems is investigated which is subjected to the iteratively applied measurements and conditional selection of a typical entanglement purification protocol. The resulting dynamics exhibits strong sensitivity to initial conditions. For one class of initial states two types of islands characterize the asymptotic limit. They correspond to a separable and a fully entangled two-qubit state, respectively, and their boundaries form fractal-like structures. In the presence of incoherent noise an additional stable asymptotic cycle appears.

T.Kiss, S. Vymetal, L.D.Toth, A. Gabris, I. Jex, and G. Alber, Phys. Rev. Lett. 107, 100501 (2011)

Entanglement and Decoherence: Fragile and Robust Entanglement

The destruction of entanglement of open quantum systems by decoherence is investigated in the asymptotic long-time limit. For this purpose a general and analytically solvable decoherence model is presented which does not involve any weak-coupling or Markovian assumption. It is shown that two fundamentally different classes of entangled states can be distinguished and that they can be in¿uenced signi¿cantly by two important environmental properties, namely, its initially prepared state and its size. Quantum states of the ¿rst class are fragile against decoherence so that they can be disentangled asymptotically even if coherences between pointer states are still present. Quantum states of the second type are robust against decoherence. Asymptotically they can be disentangled only if also decoherence is perfect. A simple criterion for identifying these two classes on the basis of two-qubit entanglement is presented.

J. Novotny, G. Alber, and I. Jex, Phys. Rev. Lett. 107, 090501 (2011)

Asymptotic Dynamics of Qubit Networks under Randomly Applied Controlled Unitary Transformations

The asymptotic dynamics of many-qubit quantum systems is investigated under iteratively and randomly applied unitary transformations. For a one-parameter family of unitary transformations, which entangle pairs of qubits, two main theorems are proved. They characterize completely the dependence of the resulting asymptotic dynamics on the topology of the interaction graph that encodes all possible qubit couplings. These theorems exhibit clearly which aspects of an interaction graph are relevant and which ones are irrelevant to the asymptotic dynamics. On the basis of these theorems, the local entropy transport between an open quantum system and its environment are explored for strong non-Markovian couplings and for different sizes of the environment and different interaction topologies. It is shown that although the randomly applied unitary entanglement operations cannot decrease the overall entropy of such a qubit network, a local entropy decrease or ¿cooling¿ of subsystems is possible for special classes of interaction topologies.

J. Novotny, G. Alber, and I. Jex, New Journal of Physics 13, 053052 (2011)

Antisymmetric multi-partite quantum states

Entanglement is a powerful resource for processing quantum information. In this context, pure, maximally entangled states have received considerable attention. In the case of bipartite qubit systems the well-known four orthonormal Bell-states are of this type. One of these Bell states, the singlet Bell-state, has the additional property of being antisymmetric with respect to particle exchange. In view of this additional symmetry, it is of interest to discuss possible generalizations of this antisymmetric Bell state to cases with more thank two particles and with single-particle Hilbert spaces involving more than two dimensions. Possible applications of this class of states include new key sharing protocols and new methods for comparing quantum states.

I. Jex, G. Alber, S. N. Barnett, and A. Delgado, Prog. Phys. 51, 171 (2003)

Universal quantum processes, entanglement and quantum copying

One of the main driving forces in the rapidly developing field of quantum information processing is the question of whether basic quantum phenomena such as interference and entanglement can be exploited for practical purposes. In this context, it has been realized that the linear character of quantum theory may impose severe restrictions on the performance of elementary tasks of quantum information processing. As a consequence it is impossible to copy (or clone) an arbitrary quantum state perfectly. In view of the significance of entangled states for many aspects of quantum information processing, the natural question arises, whether similar restrictions also hold for quantum mechanical entanglement processes.

Though many quantum processes are capable of copying or entangling some pure input states of a quantum system with a known reference state of a second quantum system, it is not easy to achieve this goal for all possible input states. In view of this difficulty, it is of particular interest to investigate universal (or covariant) processes, which are able to entangle or copy all pure input states of a quantum system which are members of a particular set or of a linear space in an optimal way. Thereby, the restrictions imposed on these processes by the linear character of quantum theory are not only of practical interest, but they also hint at fundamental limits of quantum theory itself. Most recently we have investigated the problem of the optimal copying of pure two-qubit states of a given degree of entanglement.

J. Novotný, G. Alber, and I. Jex, Phys. Rev. A 73, 062311 (2006)
J. Novotný, G. Alber, and I. Jex, Phys. Rev. A 71, 042332 (2005)
G. Alber, A. Delgado, and I. Jex, Quantum Information and Computation 1, 33 (2001)

Contact

Prof. Dr. Gernot Alber

Institut für Angewandte Physik

Hochschulstraße 4a
64289 Darmstadt, Germany

+49-6151/16-20400 (fax: 20402)

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